HDMI and DVI carry the same video signal, basically. Meaning, there's no quality loss in terms of picture and you don't get locked out of HDCP encrypted content.
However, DVI does NOT carry sound. You will need a HDMI to DVI w/ audio output adapter. These are actually quite tricky to find as many are mislabeled and won't give you want you want. It depends on your sound setup too as there's 3.5mm (headphone size) and RCA (regular white/red) options.
You specifically need an HDCP connection or your PS4 will not display if it's still the same as I think it is. That's why HDMI to DVI is the easiest.
You can do that or get an HDMI to DVI adapter (no audio) along with an optical to analog converter together. This will run you a bit more money.
HDMI to Displayport adapters are even trickier to find since you need one that's active (the adapter needs its own power source) to work with HDCP.